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On Einstein warped product space with respect to semi symmetric metric connection

Yıl 2021, Cilt: 50 Sayı: 5, 1477 - 1490, 15.10.2021
https://doi.org/10.15672/hujms.755030

Öz

In this paper, we study Einstein warped product space with respect to semi symmetric metric connection. During this study we establish some results on curvature, Ricci and scalar tensors with respect to semi symmetric metric connection and second order semi symmetric metric connection. In the last section, we investigate under what conditions, if $M$ is an Einstein warped space with nonpositive scalar curvature and compact base with respect to semi symmetric metric connection then $M$ is simply a Riemannian product space.

Teşekkür

The Second author is supported by UGC JRF of India, Ref. No: 1269/(SC)(CSIR-UGC NET DEC. 2016).

Kaynakça

  • [1] N.S. Agashe and M.R. Chafle, A semi-symmetric non-metric connection in a Rie- mannian manifold, Indian J. Pure Appl. Math. 23 (6), 399–409, 1992.
  • [2] R. Bishop and B. O’Neill, Manifolds of negative curvature, Trans. Am. Math. Soc. 145, 1–49, 1969.
  • [3] A.L. Besse, Einstein manifolds. Ergeb. Math. Grenzgeb., 3. Folge, Bd. 10. Berlin, Heidelberg, New York, Springer-Verlag. 1987.
  • [4] F. Dobarro and B, Ünal, Curvature of multiply warped products, J. Geom. Phys. 55 (1), 75–106, 2005.
  • [5] D. Dumitru, On Compact Einstein Warped Products, Annals Of Spiru Haret Univer- sity: Mathematics-Informatics Series, Bucharest, Romania, 2011.
  • [6] A. Friedmann and J.A. Schouten, Über die Geometrie der halbsymmetrischen Uber- tragungen, Math. Z. 21, 211–223, 1924.
  • [7] F.E.S. Feitosa, A.A.F. Filho and J.N.V. Gomes, On the construction of gradient Ricci soliton warped product, Nonlinear Analysis, 161, 30–43, 2017.
  • [8] S. Gallot, D. Hulin and J. Lafontaine, Riemannian Geometry, Springer-Verlag, Berlin, 1987.
  • [9] H.A. Hayden, Subspace of a space with torsion, Proc. Lond. Math. Soc. II Series, 34, 27–50, 1932.
  • [10] D.S. Kim, Compact Einstein Warped Product Spaces, Trends Math. 5 (2), 1–5, 2002.
  • [11] D.S. Kim and Y.H. Kim, On compact Einstein warped product spaces with nonpositive scalar curvature , Proc. Amer. Math. Soc. 131 (8), 2573–2576, 2003.
  • [12] M.T. Mustafa, A non-existence result for compact Einstein warped products, J. Phys. A: Math. Gen. 38, L791–L793, 2005.
  • [13] B. O’Neill, Semi-Riemannian Geometry. With Applications to Relativity, Pure and Applied Mathematics 103, Academic Press, Inc., New York, 1983.
  • [14] S. Pahan, B. Pal and A. Bhattacharyya, Multiply warped product on quasi-Einstein manifold with a semi-symmetric metric connection, Analele Universitatii Oradea Fasc. Matematica XXIV (1), 171–183, 2017.
  • [15] Q. Qu and Y. Wang, Multiply warped products with a quarter-Symmetric connection, J. Math. Anal. Appl. 431 (2), 955–987, 2015.
  • [16] K. Yano, On semi-symmetric connection, Rev. Roumaine Math Pures App. 15, 1579– 1586, 1970.
Yıl 2021, Cilt: 50 Sayı: 5, 1477 - 1490, 15.10.2021
https://doi.org/10.15672/hujms.755030

Öz

Kaynakça

  • [1] N.S. Agashe and M.R. Chafle, A semi-symmetric non-metric connection in a Rie- mannian manifold, Indian J. Pure Appl. Math. 23 (6), 399–409, 1992.
  • [2] R. Bishop and B. O’Neill, Manifolds of negative curvature, Trans. Am. Math. Soc. 145, 1–49, 1969.
  • [3] A.L. Besse, Einstein manifolds. Ergeb. Math. Grenzgeb., 3. Folge, Bd. 10. Berlin, Heidelberg, New York, Springer-Verlag. 1987.
  • [4] F. Dobarro and B, Ünal, Curvature of multiply warped products, J. Geom. Phys. 55 (1), 75–106, 2005.
  • [5] D. Dumitru, On Compact Einstein Warped Products, Annals Of Spiru Haret Univer- sity: Mathematics-Informatics Series, Bucharest, Romania, 2011.
  • [6] A. Friedmann and J.A. Schouten, Über die Geometrie der halbsymmetrischen Uber- tragungen, Math. Z. 21, 211–223, 1924.
  • [7] F.E.S. Feitosa, A.A.F. Filho and J.N.V. Gomes, On the construction of gradient Ricci soliton warped product, Nonlinear Analysis, 161, 30–43, 2017.
  • [8] S. Gallot, D. Hulin and J. Lafontaine, Riemannian Geometry, Springer-Verlag, Berlin, 1987.
  • [9] H.A. Hayden, Subspace of a space with torsion, Proc. Lond. Math. Soc. II Series, 34, 27–50, 1932.
  • [10] D.S. Kim, Compact Einstein Warped Product Spaces, Trends Math. 5 (2), 1–5, 2002.
  • [11] D.S. Kim and Y.H. Kim, On compact Einstein warped product spaces with nonpositive scalar curvature , Proc. Amer. Math. Soc. 131 (8), 2573–2576, 2003.
  • [12] M.T. Mustafa, A non-existence result for compact Einstein warped products, J. Phys. A: Math. Gen. 38, L791–L793, 2005.
  • [13] B. O’Neill, Semi-Riemannian Geometry. With Applications to Relativity, Pure and Applied Mathematics 103, Academic Press, Inc., New York, 1983.
  • [14] S. Pahan, B. Pal and A. Bhattacharyya, Multiply warped product on quasi-Einstein manifold with a semi-symmetric metric connection, Analele Universitatii Oradea Fasc. Matematica XXIV (1), 171–183, 2017.
  • [15] Q. Qu and Y. Wang, Multiply warped products with a quarter-Symmetric connection, J. Math. Anal. Appl. 431 (2), 955–987, 2015.
  • [16] K. Yano, On semi-symmetric connection, Rev. Roumaine Math Pures App. 15, 1579– 1586, 1970.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Buddhadev Pal 0000-0002-1407-1016

Pankaj Kumar Bu kişi benim 0000-0001-5778-211X

Yayımlanma Tarihi 15 Ekim 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 50 Sayı: 5

Kaynak Göster

APA Pal, B., & Kumar, P. (2021). On Einstein warped product space with respect to semi symmetric metric connection. Hacettepe Journal of Mathematics and Statistics, 50(5), 1477-1490. https://doi.org/10.15672/hujms.755030
AMA Pal B, Kumar P. On Einstein warped product space with respect to semi symmetric metric connection. Hacettepe Journal of Mathematics and Statistics. Ekim 2021;50(5):1477-1490. doi:10.15672/hujms.755030
Chicago Pal, Buddhadev, ve Pankaj Kumar. “On Einstein Warped Product Space With Respect to Semi Symmetric Metric Connection”. Hacettepe Journal of Mathematics and Statistics 50, sy. 5 (Ekim 2021): 1477-90. https://doi.org/10.15672/hujms.755030.
EndNote Pal B, Kumar P (01 Ekim 2021) On Einstein warped product space with respect to semi symmetric metric connection. Hacettepe Journal of Mathematics and Statistics 50 5 1477–1490.
IEEE B. Pal ve P. Kumar, “On Einstein warped product space with respect to semi symmetric metric connection”, Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 5, ss. 1477–1490, 2021, doi: 10.15672/hujms.755030.
ISNAD Pal, Buddhadev - Kumar, Pankaj. “On Einstein Warped Product Space With Respect to Semi Symmetric Metric Connection”. Hacettepe Journal of Mathematics and Statistics 50/5 (Ekim 2021), 1477-1490. https://doi.org/10.15672/hujms.755030.
JAMA Pal B, Kumar P. On Einstein warped product space with respect to semi symmetric metric connection. Hacettepe Journal of Mathematics and Statistics. 2021;50:1477–1490.
MLA Pal, Buddhadev ve Pankaj Kumar. “On Einstein Warped Product Space With Respect to Semi Symmetric Metric Connection”. Hacettepe Journal of Mathematics and Statistics, c. 50, sy. 5, 2021, ss. 1477-90, doi:10.15672/hujms.755030.
Vancouver Pal B, Kumar P. On Einstein warped product space with respect to semi symmetric metric connection. Hacettepe Journal of Mathematics and Statistics. 2021;50(5):1477-90.